"Justification" is a tricky word, because the case Benito Mussolini might make in front of the League of Nations or to Western reporters would be different from the reasons that Mussolini would state for domestic consumption. Further, there would certainly be factors that would not have been explicitly stated, but that in hindsight we can tell played a role.
So, for maximum informativeness and clarity, I have addressed each of these stated and unstated reasons under separate headings.
The Justification to the Western Press/ League of Nations
The origin of the Abyssinia Crisis lay in a border dispute over where Italian Somalia ended and Ethiopia (called Abyssinia at the time) began. According to a 1908 treaty, Italian territorial control was recognized in lands populated by certain Somali clans.
However, in the late 1920s, Italy established a military base at Walwal in the Ogaden region (currently 120 miles inside of the Ethiopian border). The inhabitants of the Ogaden region speak a Somali language, and are considered culturally somali.
However, Ethiopia believed that Walwal lay in their territory, and so in 1934 sent a contingent of British observers to demarcate the border, accompanied by a detachment from the Ethiopian army. When the Ethiopian-British group reached Walwal, the garrison of Somali Askaris refused to withdraw, and battle ensued.
In reaction to this incident, Italy and Ethiopia brought the matter to the League of Nations, with Italy demanding reparations for Ethiopian "agression", which Ethiopia refused. The League of Nations refused to name either party at fault, stating that both claimed control of Walwal.
So, the conflict at Walwal and Ethiopian refusal to pay reparations can be seen legalistically as the direct casus belli.
Of course, when speaking to foreign press, the Fascist government also justified the invasion as a way to suppress the practice of slavery in Ethiopia. Here, Mussolini's 8-year old son cheers on Italy's "crushing of slavery in a barbaric country" . And in this contemporary news article the Italian general DeBono is reported issuing decrees outlawing slavery in occupied territory.
Justification for the Italian people
In Italy, the defeat of the Italian army in 1896 at Adawa was a stinging humiliation, and was a very unusual instance where an African army defeated a European one. Thus, this later conflict would have strongly propelled by revanchist sentiment, attempting to wipe away the shame of the earlier defeat against Ethiopia.
In a larger context, Mussolini also justified the war as a way to expand Italy's colonial holdings saying "the destiny of Italy's future generations lies in Africa and the east". Meaning, the occupation of Ethiopia would open up opportunities for Italian migration and settlement, just as previous ventures in Libya, Eritrea and Somalia had resulted in Italian migration and settlement.
Factors not stated
Similarly, Italian colonial ventures in the late 19th century had been championed by the elements of the Catholic church in Italy, as a way of spreading Italian culture and Catholocism in Africa. The possibility of opening Ethiopia to Italian Catholicism was likely used as a justification.
Domestically, Mussolini faced an economy with high unemployment and civil unrest. In 1932, he made a speech to the Fascist Grand Council estimating that there were more than 1.1 million unemployed italians. In that same speech, he relates an anecdote about demonstrations by women, asking for government action against the economic stagnation.
So, in such a climate of civil unrest, a foreign war was an effective way of gaining short-term popularity and distracting from domestic troubles.